Uniqueness of Direct Problem Solutions of the Process: Landslide Massif Moisture Transfer Movement with Instant and Corded Sources

Abstract

This article examines the direct problem of soil moisture movement in the landslide mass as one of the primary causes of landslide occurrences. The direct problem is analyzed considering instant and corded sources, which are the most appropriate initial and boundary conditions for modeling this natural phenomenon. When studying direct problems, primary attention is given to the correctness of their solutions, including issues of existence, uniqueness, and stability of solutions. The paper outlined the uniqueness of the solution to the direct problem. The direct problem is to determine the moisture function of the landslide massif. The methods of straightening the characteristic and extracting features were used to obtain a problem with data on the characteristics. for the first time. To prove the theorem, a study was conducted using the method of energy inequalities. Using energy inequalities for hyperbolic equations, the uniqueness theorem was proven. The equations of moisture transfer motion were studied with an instantaneous source and a cord source. The equations in such a formulation are studied for the first time.

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